The breakdown of budget negotiations this week between California Gov. Jerry Brown and legislative Republicans leaves the state with a handful of options for handling the $26 billion deficit, none of them particularly attractive.

Mr. Brown had sought Republican votes to help place an initiative on the June ballot asking voters to agree to extend a handful of temporary tax increases by five years. When the governor refused to meet their terms, Republicans pulled out of the negotiations Tuesday, but that doesn’t mean the measure is dead.

Democrats, who control both houses of the legislature, could place a tax-increase proposal on the ballot before the fiscal year ends June 30.

It’s a little risky legally, however, because without Republicans, Democrats could only muster a simple majority vote. California law requires tax increases to be passed by a two-thirds vote of each house, but legal experts are divided over whether asking voters to approve a tax increase counts as a “tax increase.”

The bigger problem is whether Democrats could drum up enough votes among a cash-strapped electorate to pass a tax increase, especially without the backing of any Republican lawmakers.

A Public Policy Institute of California poll released March 23 showed voter support for the proposal waning. While 66 percent of likely voters agreed with the plan in January, only 51 percent still thought it was a good idea by March.

The survey also showed likely voters divided on how to balance the budget, with 41 percent saying they preferred a mixture of cuts and tax increases, and 40 percent favoring the so-called “all-cuts” solution.

“They seem to be convinced it will not pass,” said Tony Quinn, co-editor of the California Target Book in Sacramento. “They’ve probably got internal polling data saying that if they don’t have Republican votes, voters won’t pass it.”

Another option would be to place the tax-raise measure on the November ballot, but that election falls too late to save the state from the looming budget shortfall. Supporters also worry that voters would be less likely to approve an extension of the temporary tax increases once they expire.

Allowing the temporary taxes to expire would also push California into a deeper hole, say backers of the ballot measure.

“July 1 is the expiration of the temporary taxes, and going past that would lead to lost revenue, so you’re digging yourself into a deeper hole,” said Steve Smith, spokesman for the California Labor Federation.

The governor approved $11.2 billion in cuts last week in an effort to trim the state’s $26 billion deficit, demonstrating that he’s not looking to balance the budget on tax increases alone. Unlike governors in New York and New Jersey, who have balanced their budgets mainly through budget cuts, Mr. Brown has attempted to stake out a compromise between cuts and tax increases.

“I’m going to explore every possible avenue,” said Mr. Brown in a video message Tuesday. “There’s more than one way to get to the goal, and over the next several weeks and months, I’m going to find a way to get our budget balanced.”

Mr. Smith said labor still favors a June election in order to avoid the “all-cuts” scenario.

“That’s the nuclear option in California,” Mr. Smith said. “It would destroy so many things so many people hold dear.”

At the same time, fiscal hawks say the advantage of an “all-cuts” solution is that it would compel Democrats to make the tough choices, such as pension reform, that so far the party has been unwilling to make.

“In the meantime, they may have to live within their means,” said Jon Coupal, president of the Howard Jarvis Taxpayers Association.

The GOP had pushed for pension reform for public employees, a hard cap on state spending, and a loosening of the state’s regulatory climate. Democrats said the Republican demands were unreasonable, while Republicans blamed the state’s public-employee unions and trial attorneys for sinking the negotiations.

“As a result of these groups’ refusal to challenge the status quo, it has become clear the governor and legislative Democrats are not in a position to work with us to pass the measures necessary to move California forward,” said Republican state Sen. Anthony Cannella in a statement.

Even though the parties seem worlds apart, it’s possible negotiations could rise from the dead. The deadline for placing a measure on the June ballot would be the end of the week.

“I haven’t given up hope the Republicans might come back to the table and reconsider,” Mr. Smith said. “There’s a lot of reasons to get this done before the July 1 deadline.”